ABC incorporated,which deals with building products has accumulated sales for th

Question

ABC incorporated,which deals with building products has accumulated sales for three by five lumber(in board feet) and the number of building permits in its area for the past 10 quarters.

develop a linear regression model for these data and determine the strength of the linear relationship by using correlation. if the model appears to be relatively strong, determine the forecast for the lumber, given 10 building permits in the next quarter. Hint: you must also calculate the correlation coefficient.

Quarter Building permits(x) Lumber sales (1000 of bed.ft.) (y} 1 8 12.6 2 12 16.3 3 7 9.3 4 9 11.5 5 15 18.1 6 6 7.6 7 5 6.2 8 8 14.2 9 10 15.0 10 12 17.8

Explanation / Answer

The Regresssion equation is

y=a+bx

From Excel

The fitted Regression equation is

y=1.341 +1.252 (Building permits)

Now when x=10

Then y=1.341 +1.252 (10)

y=13.861

And The correlation between and y is 0.9255

SUMMARY OUTPUT Regression Statistics Multiple R 0.925475 R Square 0.856503 Adjusted R Square 0.838566 Standard Error 1.67644 Observations 10 ANOVA df SS MS F Significance F Regression 1 134.2004 134.2004 47.75045 0.000123 Residual 8 22.48362 2.810453 Total 9 156.684 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.340654 1.74928 0.766404 0.465447 -2.69319 5.3745 -2.69319 5.3745 Building permits(x) 1.252103 0.181197 6.91017 0.000123 0.834262 1.669944 0.834262 1.669944

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